Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the diced yellow onion and minced garlic, sautéing for 4 to 5 minutes until softened and fragrant.
Add the whole chicken breasts to the pot along with the chicken broth, drained white beans, diced green chiles, frozen corn, ground cumin, and dried oregano. Stir well to combine.
Bring the mixture to a gentle boil, then reduce the heat to medium-low. Cover the pot and let it simmer for 20 to 25 minutes, or until the chicken breasts are fully cooked through and tender.
Carefully remove the cooked chicken breasts from the pot and place them on a cutting board. Shred the meat using two forks, then return the shredded chicken to the simmering pot.
Stir in the softened cream cheese, stirring continuously until it completely melts into the broth, creating a smooth and creamy texture. Simmer for an additional 5 minutes to allow the chili to thicken slightly.
Remove the pot from the heat. Stir in the shredded cheddar cheese and fresh chopped cilantro.
Ladle the chili into bowls and serve immediately. Top with additional cheddar cheese, cilantro, avocado, or tortilla chips if desired.